混合环境中气候变化下的持久性与灭绝
Persistence versus extinction under a climate change in mixed environments
摘要：
本文研究了反应扩散方程\begin{equation} u_t-Δu=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\inΩ,\nonumber \end{equation}中物种的持续生存与绝灭，其中$Ω$为圆柱型或部分周期区域，$f$为Fisher-KPP型，标量$c>0$为给定的强迫速度.这种类型的方程最初来自种群动力学模型（参见\cite{BDNZ}、\cite{PL}、\cite{SK}），用于研究气候变化对物种持续性和灭绝的影响。从这些工作中，我们知道，动力学是由移动前$u(t,x_1,y)=U(x_1-ct,y)$，从而描述的移动前的设置起着重要的作用。在本文中，我们首先考虑一个更一般的模型比模型的\cite{BDNZ}在高维空间中，其中的环境只假设是全球不利的有利口袋延伸到无穷大。我们考虑在两个框架：反应项是时间无关或时间周期依赖。对于后者，我们研究了当$Ω$外的环境变得非常不利时的物种浓度，并进一步证明了前线的对称性破缺性质。
英文摘要：
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-Δu=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\inΩ,\nonumber \end{equation} where $Ω$ is of cylindrical type or partially periodic domain, $f$ is of Fisher-KPP type and the scalar $c>0$ is a given forced speed. This type of equation originally comes from a model in population dynamics (see \cite{BDNZ},\cite{PL},\cite{SK}) to study the impact of climate change on the persistence versus extinction of species. From these works, we know that the dynamics is governed by the traveling fronts $u(t,x_1,y)=U(x_1-ct,y)$, thus characterizing the set of traveling fronts plays a major role. In this paper, we first consider a more general model than the model of \cite{BDNZ} in higher dimensional space, where the environment is only assumed to be globally unfavorable with favorable pockets extending to infinity. We consider in two frameworks: the reaction term is time-independent or time-periodic dependent. For the latter, we study the concentration of the species when the environment outside $Ω$ becomes extremely unfavorable and further prove a symmetry breaking property of the fronts.
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